The energy spectrum of particles will help distinguish black holes from compact massive objects

Scientists from Moscow Institute of Physics and Technology (MIPT), the Institute for Theoretical and Experimental Physics, and the National Research University Higher School of Economics have devised a method of distinguishing black holes from compact massive objects that are externally indistinguishable from one another. The method involves studying the energy spectrum of particles moving in the vicinity – in one case it will be continuous and in the other it will be discrete. The findings have been published in Physical Review D.

Black holes, which were predicted by Einstein’s theory of general relativity, have an event horizon – a boundary beyond which nothing, even light, can return to the outside world. The radius of this boundary is called the Schwarzschild radius, in physical terms it is the radius of an object for which the escape velocity is greater than the speed of light, which means that nothing is able to overcome its gravity.

Black holes of stellar mass are the result of gravitational collapse which occurs at the time when a star “burns out” all its thermonuclear fuel and the force of the gas pressure can no longer resist gravity. If the star is massive enough, it collapses to a size smaller than the Schwarzschild radius and turns into a black hole. However, time on the event horizon slows down so much that for an outside observer the collapsing process almost stops (if a ship falls into a black hole, for example, to an outside observer it will appear to be continually falling toward the horizon), therefore all the black holes we see are objects that are eternally collapsing.

Astrophysicists have not yet been able to “see” a black hole directly, but there are many objects that are “suspected” of being black holes. Most scientists are sure that in the centre of our galaxy there is a supermassive black hole; there are binary systems where one of the components is most likely a black hole. However, some astrophysicists believe that there may be compact massive objects that fall very slightly short of black hole status; their range is only a little larger than the Schwarzschild radius. It may be the case that some of the “suspects” are in fact objects such as these. From the outside, however, they are not distinguishable from black holes.

Emil Akhmedov, Fedor Popov, and Daniil Kalinov devised a method to tell the difference between them, or more precisely the difference between compact massive objects and collapsing objects.

“We examined the scalar quantum field around a black hole and a compact object and found that around the collapsing object – the black hole, there are no bound states, but around the compact object there are,” explains FedorPopov, a member of staff at MIPT’s Laboratory of High Energy Physics.

He and his colleagues examined the behaviour of scalar particles (the spin of these particles is zero – an example of this could be the Higgs boson) in the vicinity of black holes and massive compact objects.

The scientists derived analytical expressions for the energy spectrum of the particles. It was found that near the surface of an ultra-compact star with a radius slightly larger than the Schwarzschild radius there is a “potential hole” – an area of space where particles fall into a gravitational “trap”. The problem in this case is then similar to a simple task in quantum mechanics where the spectrum of the particles in the potential hole needs to be found. This spectrum is discrete, i.e. it has energy values where there are no particles. In simpler terms, the potential hole does not release particles of certain energies, and an “empty space” appears in the spectrum.

In the case of a black hole in the vicinity of a Schwarzschild sphere there are no stationary potentials as there is a constant process of collapse, the boundary of the “hole” moves away and the energy spectrum is continuous.

“We scatter a beam of particles on the object and observe the spectrum. And we see that if there are no discrete levels in the spectrum, it is a black hole, and if there are – it is a compact object. Although this particular study focused on spinless particles, we can assume that the spectrum of other types of particles would behave in the same way,” says Fedor Popov.

He notes that so far this is only a theoretical study; we do not yet have the means to observe the spectra of particles in the vicinity of potential black holes – but now we are one step closer.

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